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A family of iteration with third order convergence. (Chinese. English summary) Zbl 1087.65563

Summary: A family of iterations for solving nonlinear operator equations in Banach space is presented. The family of iteration avoids evaluating the second Fréchet derivative, but it has convergence of three-orders. The convergence theorem is established using the majorant method, and meanwhile, the sharp estimates are also given.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
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